
Here \(\nabla \cdot \)  is the divergence and \(\Delta \)  is the Laplacian
operator. In general, by evolving along the Langevin dynamics, a distribution
will get closer to its target distribution \(\pi \) . From [1]}
Lemma 1, we have
\(\frac{d}{dt}(H(p_{t}|\pi ))=-\mathbb {E}_{\pi }\left\Vert \nabla \log \frac{p_{t}}{\pi }\right\Vert ^{2}.\) 
